Though I had knew "Monty Hall problem" from "Owari-monogatari(jyou)" by Ishin Nishio san, I have forgotten it.
Recently, the problem appeared again during "Bayes estimator" study, and I tried to understand this problem and answer.
So, I went to hell for the first time in a long time.
"Monty Hall problem" is easy to understand. You can fine it from many web sites.
(1)There are three doors in front of a player, and the new car of the prize is behind the door of one of them. Goats (meaning out) are behind other doors.
(2)The player gets the new car if they hit the door of the new car. Of course, the player doesn’t know which door is bingo.
(3)Monty (quizmaster) knows the door of the new car, and he shows the goat by opening one goat's door after the (2).
(4)Monty tells the players that they can have a change to change the door.
Question: Should the player change the door?
Answer: Absolutely they should change the door. The probability goes up two times.
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"What on earth?
"Why the probability goes up twice when the door is changed?"
"The bingo door has been decided at the first stage, so it should not change the probability by ex-post action?"
Do you think so?
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The woman writer got more than ten thousands letters of protest (including near one thousand doctorate degree holders) nationwide, and it became tremendous fuss.
Well, I think, would be so.
Even me, I think I did same thing.
But the woman was right.
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I did not know the reason even after reading the literature various.
So I tried to execute the simulation activation program using the Monte Carlo method.
However I tried many times again, the numeric showed that she is right.
"Heck! What is this?!
Using all of the overtime hours, I had been thinking all the way this problem.
No, no. This is an honest business.
It is necessary for me to understand "Bayesian estimation" correctly.
After all, I could understand the problem using the resolve to use "100 door’s case" deeply.
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So I hope that everybody also suffer against this problem.